Educational program

Data Science: A Roadmap for Bachelor, Master, and Doctoral Degrees

Mathematics

• Discrete analysis and graphs ***
• Abstract algebra and group theory **
• Mathematical *** and functional analysis *
• ODE, PDE, and mathematical modeling *

• Linear algebra ***
• Tensor algebra and calculus *
• Theoretical physics *
• Differential geometry and Geometric algebra *
• Scientific computation and numerical methods ***

• Measure and Probability ***
• Multivariate statistics ***
• Bayesian statistics and Graphical models **
• Stochastic processes and SDE *
• Bayesian model selection **
• Diffusion probability and flows **

Computer science

• Programming ***
• Computational differentiation **
• Software architectures **
• System analysis **
• Category theory *
• Parallel and distributed computing **

Optimization and control

• Discrete optimization **
• Convex optimization **
• Mathematical programming ***
• Optimal control**

Core of Data science

• Machine learning and data analysis
• Deep learning
• Bayesian model selection
• Bayesian multi-modeling
• Generative models (practice BS and theory MS)
• Reinforcement and online learning
• Geometric deep learning
• Geometric generative models

Applications

• Signal analysis
• Computer vision
• Audio processing
• Natural language processing
• Topic modeling and Information retrieval
• Recommender systems
• Multimedia and heterogeneous data
• Bioinformatics
• Brain-computer interfaces and metaverse

*** essential, ** recommended, * advanced 

Exams

• Ph.D. theoretical minimum for Computer science: AI and machine learning